How can I assign an image texture on a Circle?
In Edit Mode select all your faces making sure you specifically click on one of them to make it the active face.

Unwrap it using the Follow Active Quads option. 
In the UV Image Editor turn on the option Constraint to Image Bounds under the UV menu.

Rotate your unwrapped faces 90º if necessary so their orientation follows the rings.

Move them so they fit to the 0,0 coordinate then using scale resize them so they completely fit within the image boundaries. The Constraint to Image Bounds option should make sure everything snaps into place easily.